Estimation and identification of nonlinear dynamic systems

A technique is presented for processing noisy state-observable time domain measurements of a nonlinear dynamic system in order to optimally estimate both the state vector trajectory and any model error that may be present. The model error estimate may be used subsequently to accurately identify the parameters in the differential equation model of the nonlinear dynamic system. The method is demonstrated by application to several examples and is shown to be accurate and robust with respect to 1) large errors in the original assumed differential equation model, including an assumed linear model, 2) low measurement frequency, 3) low measurement accuracy (i.e., large measurement noise), and even 4) low total number of measurements.